1. Complex Algebra 1.1 Introduction 1.2 Algebra of complex numbers 1.3 Argand diagram 1.4 Different forms of complex number 1.5 De moivre?s theorem 1.6 Trigenometric, exponential and hyperbolic functions 1.7 Logarithm of a complex number 1.8 Powers and roots of a complex number 1.9 Application of complex numbers to determine velocity and acceleration 2. Vector Algebra 2.1 Introduction 2.2 Addition and subtraction of vectors 2.3 Multiplication of vectors 2.4 Scalar triple product 2.5 Geometrical interpretation of scalar triple product 2.6 Vector triple product 3. Vector Analysis 3.1 Introduction 3.2 Differentiation of a vector with respect to a scalar 3.3 Scalar and vector fields 3.4 Vector differential operator 3.5 Gradient of a scalar field 3.6 Divergence of a vector field 3.7 Curl of a vector field 3.8 Statement of gauss-divergence theorem and stoke’s theorem 3.9 Vector integrals: Line, surface and volume integral and their examples 3.10 Vector identities 4. Partial Differentiation 4.1 Introduction 4.2 Definition of partial differentiation 4.3 Successive differentiation 4.4 Total differentiation 4.5 Exact differential 4.6 Chain rule 4.7 Two theorems in partial differentiation 4.8 Change of variables from cartesian to polar co-ordinates 4.9 Implicit and explicit functions 4.10 Conditions for maxima and minima (Without Proof) 5. Differential Equation 5.1 Introduction 5.2 Frequently occurring partial differential equations [Cartesian Co-ordinates] 5.3 Terminology used in differential equations (Order, Degree, Linearity and Non–Linearity, Homogeneity and Non-Homogeneity) 5.4 Singular points of differential equation
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